### Home > APCALC > Chapter 2 > Lesson 2.3.3 > Problem 2-125

2-125.

Determine if the following functions are even, odd, or neither. Explain how you determined your choice.

**Even and Odd Functions**

A function is an

**even function**if, for all

*in its domain,*

*.*

A function is an

**odd function**if, for all

*in its domain,*

*.*

Example: If , then

Therefore , so

*is odd.*

is an odd function. Definition of odd functions:

*Therefore,*

Explore what looks like:

Hence

This is the definition of an even function: .

Test for even:

; not even

Test for odd: ...